Succinct circuit representations and leaf languages are basically the same concept

This paper connects two topics of Complexity Theory: The topic of succinct circuit representations initiated by Galperin and Wigderson, and the topic of leaf languages. A Boolean circuit c describes in a natural way the word given by the result column in the truth table representation. This way, each language A determines its succinct version S(A). It is shown for any language A that its succinct version S(A) is polynomial-time many-one complete for the leaf language defined by A. Also it is shown that if one uses for the succinct version branching programs instead of circuits then one will get complete problems for logspace classes.Postprint (published version